1.
Luminosity function
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The luminosity function or luminous efficiency function describes the average spectral sensitivity of human visual perception of brightness. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It should not be considered perfectly accurate in every case, but it is a good representation of visual sensitivity of the human eye. The CIE luminosity function y or V is a standard established by the Commission Internationale de lÉclairage. It also forms the color matching function in the CIE1931 color space. There are two luminosity functions in common use, for everyday light levels, the photopic luminosity function best approximates the response of the human eye. For low light levels, the response of the eye changes. The photopic curve is the CIE standard curve used in the CIE1931 color space, the luminous flux in a light source is defined by the photopic luminosity function. The following equation calculates the total flux in a source of light. Formally, the integral is the product of the luminosity function with the light spectrum. In practice, the integral is replaced by a sum over discrete wavelengths for which tabulated values of the luminosity function are available, the CIE distributes standard tables with luminosity function values at 5 nm intervals from 380 nm to 780 nm. The standard luminosity function is normalized to a value of unity at 555 nm. The value of the constant in front of the integral is usually rounded off to 683 lm/W, the small excess fractional value comes from the slight mismatch between the definition of the lumen and the peak of the luminosity function. The value of y is 0.999,997 at 555.016 nm, the number 683 is connected to the modern definition of the candela, the unit of luminous intensity. This arbitrary number made the new definition give numbers equivalent to those from the old definition of the candela, there have been numerous attempts to improve the standard function, to make it more representative of human vision. Judd in 1951, improved by Vos in 1978, resulted in a known as CIE VM. More recently, Sharpe, Stockman, Jagla & Jägle developed a consistent with the Stockman & Sharpe cone fundamentals. The standard scotopic luminosity function or V was adopted by the CIE in 1951, based on measurements by Wald, Color blindness changes the sensitivity of the eye as a function of wavelength
2.
International System of Units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
3.
Lumen (unit)
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The lumen is the SI derived unit of luminous flux, a measure of the total quantity of visible light emitted by a source. Lumens are related to lux in that one lux is one lumen per square meter, the lumen is defined in relation to the candela as 1 lm =1 cd ⋅ sr. A full sphere has an angle of 4π steradians, so a light source that uniformly radiates one candela in all directions has a total luminous flux of 1 cd × 4π sr = 4π cd⋅sr ≈12.57 lumens. If a light source emits one candela of luminous intensity uniformly across a solid angle of one steradian, alternatively, an isotropic one-candela light-source emits a total luminous flux of exactly 4π lumens. If the source were partly covered by an ideal absorbing hemisphere, the luminous intensity would still be one candela in those directions that are not obscured. The lumen can be thought of casually as a measure of the amount of visible light in some defined beam or angle. The number of candelas or lumens from a source also depends on its spectrum, the difference between the units lumen and lux is that the lux takes into account the area over which the luminous flux is spread. A flux of 1000 lumens, concentrated into an area of one square metre, the same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux. Mathematically,1 lx =1 lm/m2, a source radiating a power of one watt of light in the color for which the eye is most efficient has luminous flux of 683 lumens. So a lumen represents at least 1/683 watts of light power. Lamps used for lighting are commonly labelled with their output in lumens. A23 W spiral compact fluorescent lamp emits about 1, 400–1,600 lm, many compact fluorescent lamps and other alternative light sources are labelled as being equivalent to an incandescent bulb with a specific wattage. Below is a table that shows typical luminous flux for common incandescent bulbs, on September 1,2010, European Union legislation came into force mandating that lighting equipment must be labelled primarily in terms of luminous flux, instead of electric power. This change is a result of the EUs Eco-design Directive for Energy-using Products, for example, according to the European Union standard, an energy-efficient bulb that claims to be the equivalent of a 60 W tungsten bulb must have a minimum light output of 700–750 lm. The light output of projectors is typically measured in lumens, a standardized procedure for testing projectors has been established by the American National Standards Institute, which involves averaging together several measurements taken at different positions. For marketing purposes, the flux of projectors that have been tested according to this procedure may be quoted in ANSI lumens. ANSI lumen measurements are in more accurate than the other measurement techniques used in the projector industry. This allows projectors to be easily compared on the basis of their brightness specifications
4.
SI base unit
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The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011
5.
Steradian
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The steradian or square radian is the SI unit of solid angle. It is used in geometry, and is analogous to the radian which quantifies planar angles. The name is derived from the Greek stereos for solid and the Latin radius for ray and it is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol sr is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian, the steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit. A steradian can be defined as the angle subtended at the center of a unit sphere by a unit area on its surface. For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian, because the surface area A of a sphere is 4πr2, the definition implies that a sphere measures 4π steradians. By the same argument, the solid angle that can be subtended at any point is 4π sr. Since A = r2, it corresponds to the area of a cap. Therefore one steradian corresponds to the angle of the cross-section of a simple cone subtending the plane angle 2θ, with θ given by, θ = arccos = arccos = arccos ≈0.572 rad. This angle corresponds to the plane angle of 2θ ≈1.144 rad or 65. 54°. A steradian is also equal to the area of a polygon having an angle excess of 1 radian, to 1/4π of a complete sphere. The solid angle of a cone whose cross-section subtends the angle 2θ is, Ω =2 π s r. In two dimensions, an angle is related to the length of the arc that it spans, θ = l r r a d where l is arc length, r is the radius of the circle. For example, a measurement of the width of an object would be given in radians. At the same time its visible area over ones visible field would be given in steradians. Just as the area of a circle is related to its diameter or radius. One-dimensional circular measure has units of radians or degrees, while two-dimensional spherical measure is expressed in steradians, in higher dimensional mathematical spaces, units for analogous solid angles have not been explicitly named. When they are used, they are dealt with by analogy with the circular or spherical cases and that is, as a proportion of the relevant unit hypersphere taken up by the generalized angle, or point set expressed in spherical coordinates
6.
Dimensional analysis
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Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. The concept of physical dimension was introduced by Joseph Fourier in 1822, Physical quantities that are measurable have the same dimension and can be directly compared to each other, even if they are originally expressed in differing units of measure. If physical quantities have different dimensions, they cannot be compared by similar units, hence, it is meaningless to ask whether a kilogram is greater than, equal to, or less than an hour. Any physically meaningful equation will have the dimensions on their left and right sides. Checking for dimensional homogeneity is an application of dimensional analysis. Dimensional analysis is routinely used as a check of the plausibility of derived equations and computations. It is generally used to categorize types of quantities and units based on their relationship to or dependence on other units. Many parameters and measurements in the sciences and engineering are expressed as a concrete number – a numerical quantity. Often a quantity is expressed in terms of other quantities, for example, speed is a combination of length and time. Compound relations with per are expressed with division, e. g.60 mi/1 h, other relations can involve multiplication, powers, or combinations thereof. A base unit is a unit that cannot be expressed as a combination of other units, for example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the units of length. Sometimes the names of units obscure that they are derived units, for example, an ampere is a unit of electric current, which is equivalent to electric charge per unit time and is measured in coulombs per second, so 1 A =1 C/s. Similarly, one newton is 1 kg⋅m/s2, percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as 1/100, derivatives with respect to a quantity add the dimensions of the variable one is differentiating with respect to on the denominator. Thus, position has the dimension L, derivative of position with respect to time has dimension LT−1 – length from position, time from the derivative, the second derivative has dimension LT−2. In economics, one distinguishes between stocks and flows, a stock has units of units, while a flow is a derivative of a stock, in some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions
7.
Integrating sphere
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An integrating sphere is an optical component consisting of a hollow spherical cavity with its interior covered with a diffuse white reflective coating, with small holes for entrance and exit ports. Its relevant property is a scattering or diffusing effect. Light rays incident on any point on the surface are, by multiple scattering reflections. The effects of the direction of light are minimized. An integrating sphere may be thought of as a diffuser which preserves power and it is typically used with some light source and a detector for optical power measurement. A similar device is the focusing or Coblentz sphere, which differs in that it has an inner surface rather than a diffuse inner surface. The practical implementation of the sphere was due to work by R. Ulbricht. It has become an instrument in photometry and radiometry. It has the advantage over a goniophotometer for measuring the light produced by a source that total power can be obtained in a single measurement, the theory of a light-collecting cubical box was described by W. E. Sumpner in 1910. This number is the number of times a photon is scattered in the sphere, before it is absorbed in the coating or escapes through a port. This number increases with the reflectivity of the coating and decreases with the ratio between the total area of ports and other absorbing objects and the sphere inner area. To get a high homogeneity a recommended sphere multiplier is 10-25, the theory further states that if the above criteria are fulfilled then the irradiance on any area element on the sphere will be proportional to the total radiant flux input to the sphere. Absolute measurements of instance luminous flux can then be done by measuring a known light source, light scattered by the interior of the integrating sphere is evenly distributed over all angles. The integrating sphere is used in optical measurements, the total power of a light source can be measured without inaccuracy caused by the directional characteristics of the source, or the measurement device. Reflection and absorption of samples can be studied, the sphere creates a reference radiation source that can be used to provide a photometric standard. Integrating spheres are used for a variety of optical, photometric or radiometric measurements and they are used to measure the total light radiated in all directions from a lamp. An integrating sphere can be used to measure the reflectance of surfaces. The total power of a beam can be measured, free from the effects of beam shape, incident direction
8.
Photometry (optics)
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Photometry is the science of the measurement of light, in terms of its perceived brightness to the human eye. It is distinct from radiometry, which is the science of measurement of radiant energy in terms of absolute power, in modern photometry, the radiant power at each wavelength is weighted by a luminosity function that models human brightness sensitivity. Typically, this function is the photopic sensitivity function, although the scotopic function or other functions may also be applied in the same way. The human eye is not equally sensitive to all wavelengths of visible light, photometry attempts to account for this by weighing the measured power at each wavelength with a factor that represents how sensitive the eye is at that wavelength. The standardized model of the response to light as a function of wavelength is given by the luminosity function. The eye has different responses as a function of wavelength when it is adapted to light conditions, photopic vision is characteristic of the eyes response at luminance levels over three candela per square metre. Scotopic vision occurs below 2 × 10−5 cd/m2, mesopic vision occurs between these limits and is not well characterised for spectral response. Measurement of the effects of electromagnetic radiation became a field of study as early as the end of 18th century, measurement techniques varied depending on the effects under study and gave rise to different nomenclature. The total heating effect of infrared radiation as measured by thermometers led to development of radiometric units in terms of total energy, use of the human eye as a detector led to photometric units, weighted by the eyes response characteristic. Study of the effects of ultraviolet radiation led to characterization by the total dose or actinometric units expressed in photons per second. Many different units of measure are used for photometric measurements, people sometimes ask why there need to be so many different units, or ask for conversions between units that cant be converted. We are familiar with the idea that the adjective heavy can refer to weight or density, for example, offices are typically brightly illuminated by an array of many recessed fluorescent lights for a combined high luminous flux. A laser pointer has very low luminous flux but is bright in one direction. There are two systems of quantities known as photometric and radiometric quantities. Every quantity in one system has a quantity in the other system. For example, the eye responds much more strongly to light than to red. Watts are units of radiant flux while lumens are units of luminous flux, a comparison of the watt and the lumen illustrates the distinction between radiometric and photometric units. The watt is a unit of power and we are accustomed to thinking of light bulbs in terms of power in watts
9.
Light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey. Visible light, as all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term sometimes refers to electromagnetic radiation of any wavelength. In this sense, gamma rays, X-rays, microwaves and radio waves are also light, like all types of light, visible light is emitted and absorbed in tiny packets called photons and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality, the study of light, known as optics, is an important research area in modern physics. Generally, EM radiation, or EMR, is classified by wavelength into radio, microwave, infrared, the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths, when EMR interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. There exist animals that are sensitive to various types of infrared, infrared sensing in snakes depends on a kind of natural thermal imaging, in which tiny packets of cellular water are raised in temperature by the infrared radiation. EMR in this range causes molecular vibration and heating effects, which is how these animals detect it, above the range of visible light, ultraviolet light becomes invisible to humans, mostly because it is absorbed by the cornea below 360 nanometers and the internal lens below 400. Furthermore, the rods and cones located in the retina of the eye cannot detect the very short ultraviolet wavelengths and are in fact damaged by ultraviolet. Many animals with eyes that do not require lenses are able to detect ultraviolet, by quantum photon-absorption mechanisms, various sources define visible light as narrowly as 420 to 680 to as broadly as 380 to 800 nm
